Backup Trouble

Apparently I accidentally deleted my backup file from my old MacBook Pro. I just got this new one because the old one quit working. The hard drive from my old MBP is still working, so is there some way I can restore my old system profile and applications and all that on my new system with out the TimeMachine backup file? What would happen if I put my old hard drive in this new machine? Would it be able to read and start up like no problem? Could I then go and create a TimeMachine backup on an external disk, then switch out the hard drives again, reboot using my new system, and use Migration Assistant to restore my old MBP's TimeMachine Backup? Thanks to anyone who can help.